The fundamental lemma is an identity of orbital integrals that holds between elements of the Hecke algebra of a reductive group over a p-adic field and its endoscopic groups. By the trace formula, these identities are known in characteristic zero. We show how to transfer these identities to positive characteristic using motivic integration. This work extends earlier work with Cluckers and Loeser that proved a related transfer result for the unit element of the Hecke algebra.